Journal of Computer Science 7 (3): 416-420, 2011
ISSN 1549-3636
© 2011 Science Publications
Genetic Algorithm Based Proportional Integral Controller Design for Induction Motor
1
Mohanasundaram Kuppusamy and 2Rajasekar Natarajan
1
Department of Electrical and Electronics Engineering,
Sree Sastha Institute of Engineering and Technology, Chembarambakkam,
Chennai, 600123, India
2
School of Electrical Sciences,VIT University, Vellore, Tamilnadu, India
Abstract: Problem statement: This study has expounded the application of evolutionary computation
method namely Genetic Algorithm (GA) for estimation of feedback controller parameters for
induction motor. GA offers certain advantages such as simple computational steps, derivative free
optimization, reduced number of iterations and assured near global optima. The development of the
method is well documented and computed and measured results are presented. Approach: The design
of PI controller parameter for three phase induction motor drives was done using Genetic Algorithm.
The objective function of motor current reduction, using PI controller, at starting is formulated as an
optimization problem and solved with Genetic Algorithm. Results: The results showed the selected
values of PI controller parameter using genetic algorithm approach, with objective of induction motor
starting current reduction. Conclusions/Recommendation: The results proved the robustness and easy
implementation of genetic algorithm selection of PI parameters for induction motor starting.
Key words: Genetic algorithm, induction motor, evolutionary computation, controller parameters
There are many advantages that make GA attractive.
GA does not require the use of derivatives. They offer a
parallel searching of the solution space rather than the
point-by-point searching in a small region (Wieczorek
et al., 1998). Since the location of the optimal solution
is unknown before the search, it is very likely that the
point-by-point search needs to search through the entire
solution space in order to find the optimal solution, not
mention the traps of the local optima. Hence, GA can find
near-optimal solution for a complex problem very quickly.
INTRODUCTION
The squirrel cage induction motor is basically a
simple, less costly and reliable drive and can provide
excellent characteristics at a constant shaft speed.
Probably the cheapest and most reliable scheme of
speed control of induction motors is stator voltage
control using back-to-back connected SCRs. This
scheme is widely used for certain types of loads such as
fan and pump drives. It was shown that speed ranges of
5-1 can be easily obtained using this method (Paice,
1968; Lipo, 1971). However, little attention is being
paid to the design of controller for closed loop variable
speed operation using the above scheme. The drawback
of is that an analytical relationship could not be
established between induction motor torque and applied
voltage with thyristor excitation and only an empirical
approach was used (Shepherd and Stanway, 1967).
Further, motor parameter variation with different
operating points is not considered.
Genetic Algorithm is a stochastic search techniques
based on the mechanism of natural selection and natural
genetics. GA (Kangrang and Chaleeraktrakoon,
2007) perform search for a multidimensional space
containing a hyper surface known as the fitness surface.
Problem formulation: Induction motor starting at
rated current (Say, 1958) is formulated as an
optimization problem and is given below:
Minimize:
F ( ) =│Ir-I│
(1)
Subjected to:
min ≤
Where:
Ir =
≤
max
rated motor current
Corresponding Author: Mohanasundaram Kuppusamy, Department of Electrical and Electronics Engineering, Sree Sastha
Institute of Engineering and Technology, Chembarambakkam, Chennai, 600123, India Tel: +91
9600047399
416
J. Computer Sci., 7 (3): 416-420, 2011
I =
Φs =
min and
max
motor current
{Kp, Ki}
= refer to minimum and maximums of
For the evaluation of objective function F ( ), the
MATLAB model of induction motor is developed to
work in the closed loop starting mode (Sundaram et al.,
2009) and this is shown in the Fig. 1. Here, PI
controller block (Hassanzadeh et al., 2008) refers to
controller constants to be identified.
Implementation of GA for optimization: The primary
concept of GA was first proposed by Dr. Holland in
1975.
GA
constitutes
biologically
inspired
multiparameter
search/optimization
algorithms
(Subramanian et al., 2010) that have proven to be effective
in solving a variety of complex problems where other
algorithms have either failed or faced difficulties.
The following steps describe how the GA is designed
and applied to the present problem. Various components
of GA (Wurtz et al., 1997) such as chromosomes, fitness
function, reproduction, crossover and mutation as applied
to the present work are illustrated.
Step1: Create a population of initial solution of
parameters (kp, ki): This step primarily requires the
population size. Each variable in the problem is called
as a gene and in the present problem, there are two (i.e.,
kp, ki) genes. A Chromosome consists of the genes and
thus each chromosome represents a solution to the
problem. This is illustrated in Fig. 2.
The population consists of a set of chromosomes. It
is well articulated in literature that a population size of
5-30 is an ideal one and hence population size is
selected as 8 in this study.
Step 2: Evaluation of objective function: In the
present problem, the starting current of induction motor
is to be maintained at rated value while starting. For
each chromosome, the MATLAB model given in
Fig. 1. is simulated and F ((φ)) is computed.
Step 3: Evaluation of fitness function: The degree of
“goodness” of a solution is qualified by assigning a
value to it. This is done by defining a proper fitness
function to the problem. Since GA can be used only for
maximization problems, the following fitness function
is used:
Fitness function =1/ (1+ F ( ))
(2)
Fig. 1: Matlab/Simulink model of A.C. voltage
controller fed induction motor with PI
controller
Fig. 2: Chromosome structure
Step 4: Generation of offspring: Offspring is a new
chromosome obtained through the steps of selection,
crossover and mutation. After fitness of each
chromosome is computed, parent solutions are selected
for reproduction. It emulates the survival of the fittest
mechanism in nature. The Roulette wheel selection is
the most common and easy-to-implement selection
mechanism. A virtual wheel is implemented for this
selection process. Each chromosome is assigned a
sector in this virtual wheel and the area of the sector is
proportional to their fitness value. Thus the
chromosome with largest fitness value will occupy
largest area, while the chromosome with a lower value
takes the slot of a smaller sector. Let there be five
chromosomes labeled as A, B, C, D and E and their
fitness value increases in the order of D, B, A, E and C.
Then Fig. 3 shows a typical allocation of five sectors of
chromosomes in the Roulette wheel.
In Roulette wheel selection, an angle is generated
randomly and the chromosome corresponding to
this angle is selected. Figure 3b shows a randomly
417 J. Computer Sci., 7 (3): 416-420, 2011
(a)
(b)
Fig. 3: (a) Typical allocation of sectors for
Chromosomes; (b) Roulette wheel selection
generated angle of 4 π /3 rad. In this case, chromosome
C is selected. The chromosomes thus selected are called
parent population and are subjected to undergo
crossover and mutation to produce offspring for the
next generation. Roulette wheel selection is the
conventional method adopted in GA for selection.
Following the selection of parent population, crossover
and mutation are performed to generate offspring
population. In crossover, randomly selected subsections of two individual chromosomes are swapped to
produce the offspring. In this study, single point
crossover is used for children generation.
Mutation is another genetic operation by which a
bit within a chromosome may toggle to the opposite
binary. Figure 4 illustrates crossover and mutation. The
crossover and mutation are performed based on the
probability of crossover and mutation.
Step5: Replace the current population with the new
population.
Step6: Terminate the program if termination criterion is
reached; else go to step 2
RESULTS
For the implementation of GA to the present
problem, dedicated software in MATLAB is developed.
The parameters of GA such as crossover probability,
mutation probability, population size and number of
generations are usually selected by means of trial and
error process to achieve the best solution set. The
parameters used in the implementation of GA are listed
below:
(a)
Population size:
Coding:
Number of generations:
Selection scheme:
Crossover operator:
Crossover probability:
Mutation probability:
Termination criterion:
(b)
Fig. 4: (a) Crossover and (b) mutation
8
Binary
80
Roulette wheel
Selection
Single point
Crossover
0.7
0.01
80 iterations.
Dedicated software is developed in MATLAB for
this optimization problem and the results are analyzed.
The convergence characteristics with GA are plotted in
Fig. 5 and 6. It can be seen that the objective function
value converges to a reasonably low value of 0.03
against its ideal value of zero at 45th iteration.
418 J. Computer Sci., 7 (3): 416-420, 2011
With these controller constants, induction motor
starting is simulated using MATLAB model shown in
Fig. 1. It is seen that the motor current is almost kept
constant at its rated value during starting. This
demonstrates the effectiveness of the proposed approach.
CONCLUSION
Fig. 5: Variation of objective function
The main objective of this study is tuning of the PI
controller parameters by Genetic algorithm. Simulation
results with PI controller are included. The parameters
of PI controller are tuned using the proposed
optimization algorithm.
REFERENCES
Hassanzadeh, I., S. Mobayen and A. Harifi, 2008.
Input-output feedback linearization cascade
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(a)
(b)
Fig. 6: Variation of parameters (a) Kp; (b) Ki
The convergence is observed to be at a stable and faster
rate. The variation of controller parameters is delineated
in Fig. 6.
DISCUSSION
It is interesting to study the convergence behavior
of GA as given in Fig. 6. It is seen that, the number of
iterations required for all chromosomes to reach this
near-global optima is reasonably low. It is also seen that
the parameters of controller are suitably modified at
iterative step with the sole aim of minimizing the
objective function value. At the end of 50 generations,
the constants of controller are obtained as:
Kp= 10.3 and Ki= 2.2
Kangrang, A. and C. Chaleeraktrakoon, 2007.
Genetic algorithms connected simulation with
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10.3844/ajassp.2007.73.79
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